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210 ON THE CONDUCTION OF HEAT IN CRYSTALS.
from whence the flux in any direction may be obtained by means of the formula (1). The formulae (7) contain the expressions for the flux which result from the theory of M. Duhatnel. The constants A, B, 0, denote what may be called the principal conductivities of the crystal. The reader may suppose for the present that the following investigations are restricted to media which are symmetrical with respect to two rectangular planes.
7. It may be worth while to return to the coordinates #', y'9 z, which have a general direction, and examine the general expressions for the flux which correspond to the formulae (7). Putting fx> fy> fz> ^or ^e fluxes across planes perpendicular to the axes of of, yf, z, we get from (1) and (7)
from whence the expressions for J?', E't and (7, Ff> may be written down by symmetry.
8. So long as we are only concerned with the succession of temperatures in an infinite solid, we have no occasion to consider the flux of heat, and the general equation (5) will enable us to perform all the requisite calculations. In this equation the indestructibility* of heat is recognized, but riot its identity. If we discard the latter idea, it is nonsense to talk of the heat gained, we will suppose, by a given element of the solid, as having come from this quarter rather than from that. If we denote by A/a-, A/,/, A/2 the quantities by which the values of fX)fy)fz given by (6) exceed those given by (7), we have
dx dy dz '
* According to the very important researches of Mr Joule, work is convertible into heat, from which there can be little doubt that conversely heat is convertible into work. As regards the present investigation, however, it is perfectly immaterial whether heat be indestructible, or only not destroyed, or rather whether it be not convertible into anything else, or only not converted.